Nonlinear Theory of Elastic Plates

Nonlinear Theory of Elastic Plates provides the theoretical materials necessary for the three plate models—Cosserat plates, Reissner-Mindlin plates and Kirchhoff-Love plates— in the context of finite elastic deformations. One separate chapter is devoted to the linearized theory of Kirchhoff-Love plates, which allows for the study of vibrations of a pre-stressed plate and the static buckling of a plate. All mathematical results in the tensor theory in curvilinear coordinates necessary to investigate the plate theory in finite deformations are provided, making this a self-contained resource.

Presents the tricky process of linearization, which is rarely dealt with, but explained in detail in a separate chapterOrganized in a mathematical style, with definitions, hypotheses, theorems and proofs clearly statedPresents every theorem with its accompanying hypotheses, enabling the reader to quickly recognize the conditions of validity in results

1. Fundamentals of tensor theory 2. Initial position of a plate 3. Theory of Cosserat plates 4. Theory of Reissner-Mindlin plates 5. Theory of Kirchhoff-Love plates 6. Constitutive laws for plates 7. Linearized theory of Kirchhoff-Love plates